Find the equation of tangents of the parabola `y^2=12 x ,` which passes through the point (2, 5).

Explanation

The equation of the given parabola is `y^(2)=12x` (1)
Comparing with `y^(2)=4ax`, we get a = 3.
Therefore, the equation of the tangent from (2,5) is
`y=mx+(3)/(m)` (2)
Tangent passes through the point (2,5). Then `5=2m+(3)/(m)`
`or2m^(2)-5m+3=0`
`orm=1,(3)/(2)`
Therefore, from (2), the equations of the required tangents are
`y=x+3and2y=3x+4`